A New Approach to the Family Structure

In this letter, we introduce a new approach to formulate the family structure of the standard model. Trying to mimic the highly contrained representation structure of the standard model while extending the symmetry, we propose a SU (4) H ⊗ SU (3) C ⊗ SU (2) L ⊗ U (1) X model which upon symmetry breaking gives the three-family standard model, with the Higgs supermultiplets for incoporating supersymmetry. The hypercharge embedding is non-trivial. The model holds promise of a very interesting phenomenology. A comparison with other approaches is given. 1 In this letter, we introduce a new approach to the much pursued, however still mysterious , family problem. Trying to mimic the highly contrained group representation structure of the standard model while extending the symmetry, we propose a SU(4) H ⊗ SU(3) C ⊗ SU(2) L ⊗ U(1) X model which, upon symmetry breaking, gives the three-family standard model together with some extra vector-like states. Details of the representation content are given in table 1. To set the stage and facilitate comparison, we first try to summarize the state of art of the problem, before we describe our model-building approach. The matter content of the phenomenologically very successful standard model(SM) consists of three sets (families) of 15 chiral fermion states of identical quantum numbers. In addition, a scalar doublet Higgs is needed to break the electroweak(EW) symmetry and give the fermions masses. The existence of the scalar leads to the hierarchy problem, which is widely believed to be addressed by supersymmetry(SUSY). SUSY then doubles the particle spectrum, giving, in particular, scalar partners to fermions. Moreover, one extra Higgs doublet is needed; and the Higgses get fermionic partners. The representation structure of a single family of chiral fermions is very strongly constrained by the requirement of cancellation of all (triangle) gauge anomalies, making it easily " derivable " once some simple assumptions are taken [1]. However, the existence of three families, with the great hierarchy of masses among the fermions after EW-symmetry breaking, remains a mystery. The Higgs sector is another puzzle. There is for example no reason to enforce a minimal content a priori [2]. In the SUSY scenario, the minimal two Higgs doublets formed a vector